A Parallel Gauss–Seidel Method for Block Tridiagonal Linear Systems
Pierluigi Amodio, Francesca Mazzia · SIAM Journal on Scientific Computing · 1995
A parallel variant of the block Gauss–Seidel iteration is presented for the solution of block tridiagonal linear systems. In this method parallel computations derive from a block reordering of the coefficient matrix similar to that of the domain decomposition methods. It has been proved that the parallel Gauss–Seidel iteration has the same spectral properties of the sequential method and may be used for any sparsity pattern of the blocks of the linear system. The parallel algorithm is applied to the solution of linear systems arising from initial value problems when solved by means of boundary value methods and from elliptic partial differential equations.